Development of a Wind Turbine Test Rig and

Rotor for Trailing Edge Flap Investigation

by

Ahmed Abdelrahman

A thesis

presented to the University of Waterloo

in fulfillment of the

thesis requirement for the degree of

Masters of Applied Science

in

Mechanical Engineering

Waterloo, Ontario, Canada, 2014

©Ahmed Abdelrahman 2014

ii

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any

required final revisions, as accepted by my examiners.

I understand that my thesis may be made electronically available to the public.

iii

Abstract

Alleviating loads on a wind turbine blades would allow a reduction in weight, and potentially increase the

size and lifespan of rotors. Trailing edge flaps are one technology proposed for changing the aerodynamic

characteristics of a blade in order to limit the transformation of freestream wind fluctuations into load

fluctuations within the blade structure. An instrumented wind turbine test rig and rotor were developed to

enable a wide-range of experimental set-ups for such investigations. The capability of the developed system

was demonstrated through a study of the effect of stationary trailing edge flaps on blade load and

performance. The investigation focused on measuring the changes in flapwise bending moment and power

production for various trailing edge flap parameters. The blade was designed to allow accurate

instrumentation and customizable settings, with a design point within the range of wind velocities in a large

open jet test facility. The wind facility was an open circuit wind tunnel with a maximum velocity of 11m/s

in the test area. The load changes within the blade structure for different wind speeds were measured using

strain gauges as a function of flap length, location and deflection angle. The blade was based on the S833

airfoil and is 1.7 meters long, had a constant 178mm chord and a 6o pitch. The aerodynamic parts were 3D

printed using plastic PC-ABS material. The total loading on the blade showed higher reduction when the

flap was placed further away from the hub and when the flap angle (pitching towards suction side) was

higher. The relationship between the load reduction and deflection angle was roughly linear as expected

from theory. The effect on moment was greater than power production with a reduction in moment up to

30% for the maximum deflection angle compared to 6.5% reduction in power for the same angle. Overall,

the experimental setup proved to be effective in measuring small changes in flapwise bending moment

within the wind turbine blade.

iv

Acknowledgements

I would like to thank my supervisor Prof. David Johnson. Prof. Johnson provided an exemplary balance

between allowing creativity and independence in research work and providing guidance throughout the

process. He was always keen and supportive in helping me showcase my work with confidence whenever

there was an opportunity. I would like to thank Curtis Knischewsky who was a research assistant in our

group during the most crucial time of the development of this project. Curtis put in great effort to support

my project and his work was not just instrumental to its success, but was also done with great interest and

produced with the best quality. I would also like to thank my research group colleagues, Nigel Swytink-

Binnema, Nicholas Tam and Kobra Gharali for providing me with all the assistance I needed whenever I

approached them for help. The contribution of the Mechanical Engineering department’s electronic

technologist Andy Barber is greatly appreciated. I would like to thank all my friends that helped me

throughout my work and especially Omar Abdalla for providing crucial support during the tough final phase

of writing this thesis. I would like to mention my appreciation to all my mentors and teachers that helped

me acquire the skills and knowledge to successfully navigate through my educational career. Finally and

most importantly I would like to thank my family, namely Prof. Hamdy Abdelrahman, my father, and Dr.

Eman Elshawy, my mother and all my siblings for helping me when I needed it most, keeping me motivated,

and ensuring that I keep going forward to accomplish my dreams.

v

Dedication

To my Family.

vi

Table of Contents

List of Figures ............................................................................................................................................... x

List of Tables ............................................................................................................................................. xiv

Nomenclature ............................................................................................................................................. xvi

Acronyms ................................................................................................................................................. xviii

Chapter 1 Background .................................................................................................................................. 1

1.1 Introduction ......................................................................................................................................... 1

1.2 Project Motivation .............................................................................................................................. 2

1.3 Thesis objectives and outline .............................................................................................................. 3

Chapter 2 Literature Review ......................................................................................................................... 5

2.1 Theory ................................................................................................................................................. 5

2.1.1 Wind turbine overview ................................................................................................................. 5

2.1.2 Airfoil concepts and terminology ................................................................................................ 7

2.1.3 Aerodynamics of HAWTs ......................................................................................................... 10

2.1.4 Wind Turbine Loads .................................................................................................................. 21

2.1.5 Aerodynamic load distribution on HAWT blades ..................................................................... 23

2.1.6 Types of aerodynamic load control ............................................................................................ 30

2.1.7 Effect of TEFs ............................................................................................................................ 31

2.2 Related work ..................................................................................................................................... 35

2.2.1 Atmospheric testing of stationery TEFs ..................................................................................... 35

2.2.2 Power regulation using TEFs ..................................................................................................... 39

2.2.3 Dynamic load alleviation ........................................................................................................... 41

Chapter 3 Wind Turbine Test Rig ............................................................................................................... 43

3.1 General design requirements ............................................................................................................. 43

3.2 Specific design constraints ................................................................................................................ 45

vii

3.3 Component Selection ........................................................................................................................ 47

3.3.1 Motor and brake ......................................................................................................................... 47

3.3.2 Gearbox ...................................................................................................................................... 47

3.3.3 Electrical and control systems .................................................................................................... 47

3.3.4 Bearings ..................................................................................................................................... 48

3.3.5 Torque sensor and couplings ...................................................................................................... 49

3.4 Component Design and fabrication ................................................................................................... 50

3.4.1 Drive-shaft ................................................................................................................................. 50

3.4.2 Nacelle frame ............................................................................................................................. 51

3.4.3 Drive-train alignment ................................................................................................................. 53

3.4.4 Hub ............................................................................................................................................. 55

3.4.5 Nacelle cover ............................................................................................................................. 57

3.4.6 Tower ......................................................................................................................................... 59

3.5 Test rig Assembly ............................................................................................................................. 62

3.6 Connections and communications .................................................................................................... 64

3.7 Assembled test rig final specifications .............................................................................................. 65

Chapter 4 Modular 3D Printed Blade ......................................................................................................... 66

4.1 General design requirements ............................................................................................................. 66

4.2 Specific design constraints ................................................................................................................ 67

4.3 Aerodynamic design ......................................................................................................................... 68

4.3.1 Airfoil selection ......................................................................................................................... 68

4.3.2 Geometry determination ............................................................................................................ 69

4.4 Structural design and fabrication ...................................................................................................... 70

4.4.1 3D printing ................................................................................................................................. 71

4.4.2 Structural design ........................................................................................................................ 72

4.4.3 Aerodynamic blade sections ...................................................................................................... 72

4.4.4 TEFs ........................................................................................................................................... 76

4.4.5 Tubular Spar ............................................................................................................................... 77

4.4.6 Hub connectors .......................................................................................................................... 79

4.4.7 Control-rod ................................................................................................................................. 79

4.4.8 Full blade assembly .................................................................................................................... 80

4.4.9 Counter weight design and assembly ......................................................................................... 82

viii

4.5 Nose-cone ......................................................................................................................................... 82

4.6 Final Assembled rotor specifications ................................................................................................ 83

Chapter 5 Experimental Procedure ............................................................................................................. 87

5.1 Facility .............................................................................................................................................. 87

5.1.1 Facility Velocity Measurements. ............................................................................................... 89

5.2 Apparatus and Control Parameters ................................................................................................... 90

5.3 Instrumentation and Measurements .................................................................................................. 91

5.3.1 Strain Measurement ................................................................................................................... 91

5.3.2 Power Measurement ................................................................................................................... 92

5.3.3 Wind Measurement .................................................................................................................... 93

5.4 Calibration Procedure ....................................................................................................................... 93

5.5 Experimental Procedure .................................................................................................................... 95

5.5.1 Data Recording and Processing ................................................................................................. 98

5.5.2 Data plotting ............................................................................................................................... 99

Chapter 6 Results and Discussion ............................................................................................................. 101

6.1 Qualitative Results .......................................................................................................................... 101

6.1.1 Rig Performance ...................................................................................................................... 101

6.1.2 3D Printed blade structural integrity ........................................................................................ 102

6.2 Strain gage calibration results ......................................................................................................... 103

6.3 Wind Speed Measurements ............................................................................................................. 104

6.4 Baseline Blade Performance ........................................................................................................... 105

6.4.1 Power Readings ....................................................................................................................... 105

6.4.2 Strain Gage Readings ............................................................................................................... 106

6.5 Effect of changing the flap angle .................................................................................................... 110

6.5.1 Moment vs. wind speed ........................................................................................................... 110

6.5.2 Moment vs. radial location ....................................................................................................... 113

6.5.3 Moment and power change vs. flap deflection angle ............................................................... 114

6.6 Effect of changing length and location of flaps .............................................................................. 115

6.6.1 Moment vs. wind speed ........................................................................................................... 115

6.6.2 Moment distributions along blade span ................................................................................... 118

6.6.3 Moment vs. radial location ....................................................................................................... 120

6.6.4 Moment change vs. relative flap location ................................................................................ 121

ix

Chapter 7 Conclusion ................................................................................................................................ 122

7.1 Test turbine rig ................................................................................................................................ 122

7.1.1 Improvements to the setup ....................................................................................................... 122

7.2 Blade fabrication ............................................................................................................................. 123

7.3 Instrumentation and data acquisition .............................................................................................. 123

7.4 Trailing edge flap effects ................................................................................................................ 124

7.5 Future work ..................................................................................................................................... 125

Bibliography ............................................................................................................................................. 126

Appendix A Dimension Drawings......................................................................................................... 131

Appendix B PROPID ............................................................................................................................ 135

Appendix C Calibration data ................................................................................................................. 138

Appendix D Test rig safety & maintenance........................................................................................... 140

Appendix E Uncertainty Analysis ......................................................................................................... 141

x

List of Figures

Figure 1.1 Illustration of a hinged trailing edge flap on an S833 airfoil. ...................................................... 2

Figure 1.2 Wind Turbine diameter size development. .................................................................................. 2

Figure 2.1 Main wind turbine components. .................................................................................................. 6

Figure 2.2 Airfoil nomenclature.................................................................................................................... 7

Figure 2.3 Airfoil forces. .............................................................................................................................. 8

Figure 2.4 Typical 𝐶𝑙 vs. 𝛼. .......................................................................................................................... 9

Figure 2.5 Actuator disk model of a wind turbine. ..................................................................................... 11

Figure 2.6 Annular control volume. ............................................................................................................ 13

Figure 2.7 Blade element velocities. ........................................................................................................... 14

Figure 2.8 Blade element forces. ................................................................................................................ 15

Figure 2.9 𝐶𝑃 and 𝐶𝑇 for an ideal HAWT vs. axial induction factor 𝑎...................................................... 18

Figure 2.10 Aerodynamic, gravitational and inertial loads that affect a HAWT blade .............................. 22

Figure 2.11 Rotor forces co-ordinates and technical terms ......................................................................... 24

Figure 2.12 Modelled tangential and axial force distribution for WKA-60 turbine blade. ....................... 25

Figure 2.13 Schematic showing the coning angle Φ. ................................................................................. 26

Figure 2.14 Moment at any location 𝛽 along the blade span. ..................................................................... 28

Figure 2.15 Predicted and measured bending moments of a MOD-2 turbine blade. .................................. 29

Figure 2.16 Normalized moment distribution along the T40 and MOD-2 blade. ....................................... 30

Figure 2.17 Some typical high-lift devices ................................................................................................. 31

Figure 2.18 Effect of flap deflection on lift coefficient .............................................................................. 32

Figure 2.19 Contribution to total lift of a flapped cambered airfoil. ........................................................... 33

Figure 2.20 Aerodynamic characteristics of the NACA 66(215)-216 airfoil with a 20% flap ................... 34

Figure 2.21 Maximum lift coefficients for two distinct airfoils .................................................................. 34

xi

Figure 2.22 Variable span aerodynamic device deflection . ....................................................................... 35

Figure 2.23 Test blade dimensions ............................................................................................................. 36

Figure 2.24 Single-bladed down-wind rotor used for investigation ........................................................... 36

Figure 2.25 Sample data showing averaged data and the variation. ........................................................... 38

Figure 2.26 Blade parameters as a function or radius used for the blade design ........................................ 40

Figure 2.27 TEF angles to regulate the power above rated conditions. ...................................................... 40

Figure 3.1 Image of previous Test Turbine Rig .......................................................................................... 44

Figure 3.2 Single vs. two bearing reactions. ............................................................................................... 49

Figure 3.3 Shaft protrusion. ........................................................................................................................ 50

Figure 3.4 Nacelle frame features. .............................................................................................................. 51

Figure 3.5 Nacelle frame and adjustment plates. ........................................................................................ 52

Figure 3.6 Drive-train alignment plan. ........................................................................................................ 53

Figure 3.7 Assembled Nacelle Components (without cover) ..................................................................... 54

Figure 3.8 hub to drive-shaft assembly. ...................................................................................................... 55

Figure 3.9 Front view 3D model and image of Hub assembly showing bolt patterns. ............................... 56

Figure 3.10 Image of assembled rotor using new hub design and Gertz blades. ........................................ 56

Figure 3.11 Nacelle cover side and front view comparison, all dimensions in mm. .................................. 57

Figure 3.12 Nacelle cover images. .............................................................................................................. 58

Figure 3.13 Assembled nacelle cover 3D model and image. ...................................................................... 58

Figure 3.14 Static forces stress analysis of test rig tower. .......................................................................... 60

Figure 3.15 Dynamic forces for frequency analysis of test rig tower. ........................................................ 60

Figure 3.16 Tower main dimensions and features. ..................................................................................... 61

Figure 3.17 Tower image (side view). ........................................................................................................ 61

Figure 3.18 Test rig main components. ....................................................................................................... 62

Figure 3.19 Fully assembled wind turbine test rig images with Gertz rotor. .............................................. 63

Figure 3.20 Test Rig Communications ....................................................................................................... 64

Figure 4.1 NREL S833 airfoil ..................................................................................................................... 69

Figure 4.2 3D model vs. photo of manufactured prototype of the blade tip section. .................................. 72

Figure 4.3 Standard blade section. .............................................................................................................. 73

Figure 4.4 Blade flap section. ..................................................................................................................... 73

xii

Figure 4.5 Blade section internal details. .................................................................................................... 74

Figure 4.6 Aerodynamic blade sections assembly onto main spar. ............................................................ 75

Figure 4.7 Image of blade section showing SG slots .................................................................................. 75

Figure 4.8 Strain gage possible locations. ................................................................................................... 76

Figure 4.9 Trailing edge flap. ..................................................................................................................... 76

Figure 4.10 Image of printed blade flap section and trailing edge flaps. .................................................... 77

Figure 4.11 Spar cross-sectional location. .................................................................................................. 77

Figure 4.12 Support spar forces. ................................................................................................................. 78

Figure 4.13 Hub attachment blocks ............................................................................................................ 79

Figure 4.14 Control-rod .............................................................................................................................. 80

Figure 4.15. Blade and hub assembly. ........................................................................................................ 81

Figure 4.16 Counter-weights ...................................................................................................................... 82

Figure 4.17 Nose-cone assembly ................................................................................................................ 83

Figure 4.18 3D model and image of assembled rotor. ................................................................................ 84

Figure 4.19 3D model of assembled test rig and rotor ................................................................................ 85

Figure 4.20 Image of assembled test rig and rotor ...................................................................................... 86

Figure 5.1 Fan discharge plenum showing conditioning screens and exit plane. ....................................... 88

Figure 5.2 Facility geometry ....................................................................................................................... 89

Figure 5.3 Strain gage placement on steel spar. .......................................................................................... 91

Figure 5.4 Strain gage group locations ...................................................................................................... 91

Figure 5.5. Image showing strain gage group locations. ............................................................................. 92

Figure 5.6. Images of the strain gage setup and wiring on the blade spar. ................................................. 92

Figure 5.7. Image showing flap section sliding into position. .................................................................... 96

Figure 5.8. Image showing flap at a negative deflection angle. .................................................................. 96

Figure 5.9. Schematic identifying different flap formations and strain gage grouplocations.. .................. 97

Figure 6.1. Power vs. Wind speed (W) for the baseline case compared to PROPID predictions. ............ 105

Figure 6.2. PROPID angle of attack distribution ...................................................................................... 106

Figure 6.3. Force contributing to moment reading at SG3. ...................................................................... 107

Figure 6.4. Moment (𝑀𝑟) vs. Wind speed (W) for the baseline case. ...................................................... 108

Figure 6.5. Angle of attack (𝛼) vs. Wind speed (W) at mid-span. ............................................................ 108

xiii

Figure 6.6. Moment (𝑀𝑟) vs. radial position (𝑟) for the baseline case. .................................................... 109

Figure 6.7. Normalized moment (𝑅𝑀𝑟) vs. normalized radial position.. ................................................. 110

Figure 6.8. Moment (𝑀𝑟) vs. Wind speed (W) with the F2A activated at -5o and 5o ............................... 111

Figure 6.9. Moment (𝑀𝑟) vs. Wind speed (W) with the F2A activated at each 𝜂 .................................... 112

Figure 6.10. The increment change in flapwise bending moment measured at each 𝜂............................. 113

Figure 6.11. A comparison between the power and root moment reduction ............................................ 114

Figure 6.12. Shed vortex effect. ................................................................................................................ 115

Figure 6.13. Moment (𝑀𝑟) vs. Wind speed (W) with the single flap formations (F1𝑋) .......................... 116

Figure 6.14. Moment (𝑀𝑟) vs. Wind speed (W) for all formations .......................................................... 117

Figure 6.15. Coning angle effect. .............................................................................................................. 118

Figure 6.16. Moment (𝑀𝑟) vs. radial position (r) for each formation ...................................................... 119

Figure 6.17. Normalized moment (𝑅𝑀𝑟) vs. radial position (r/R) for each formation .............................. 119

Figure 6.18. The value change in moment (Δ𝑀𝑟) for each flap formation ............................................... 120

Figure 6.19. Percentage moment change for single flap formations. ........................................................ 121

Figure A.1. Tower dimensions drawing, inches. ...................................................................................... 131

Figure A.2 Nacelle frame dimensions drawings, inches. .......................................................................... 132

Figure A.3 Nacelle cover sheet metal parts. ............................................................................................. 133

Figure A.4. Shaft dimensions in mm. ....................................................................................................... 134

Figure C.1. Linear fit for select calibration data. ...................................................................................... 139

Figure E.1. Error bar plot for moment readings. ....................................................................................... 143

xiv

List of Tables

Table 2.1 PROPID primary user specified parameters for analysis case. ................................................... 20

Table 2.2 PROPID analysis output. ............................................................................................................ 21

Table 2.3 Device configurations for testing ............................................................................................... 37

Table 3.1 Test rig design constraints .......................................................................................................... 46

Table 3.2 Operational frequency ranges ..................................................................................................... 46

Table 3.3 Sub-panel features. ...................................................................................................................... 48

Table 3.4 Final tower specifications ........................................................................................................... 61

Table 3.5 Final test rig specifications ......................................................................................................... 65

Table 4.1 Rotor design constraints .............................................................................................................. 68

Table 4.2 PROPID input parameters. .......................................................................................................... 70

Table 4.3 3D printer specifications ............................................................................................................. 71

Table 4.4 Assembled rotor geometric specifications .................................................................................. 83

Table 5.1 UW Facility fan specifications .................................................................................................... 87

Table 5.2 UW wind facility geometry details ............................................................................................. 88

Table 5.3 Velocity measurements over a range of fan settings ................................................................... 90

Table 5.4 Control parameters ...................................................................................................................... 90

Table 5.5 Measurements Summary ............................................................................................................. 93

Table 5.6 Calibration test load locations ..................................................................................................... 94

Table 5.7 Measurement Points. ................................................................................................................... 98

Table 5.8 Recorded Data Format and Processing ....................................................................................... 99

Table 5.9 Measurement radial locations. .................................................................................................... 99

xv

Table 5.10 Measurement parameters naming and equations. ................................................................... 100

Table 6.1 Calibration results for tip applied load ...................................................................................... 103

Table 6.2 Test Wind Speeds ..................................................................................................................... 104

xvi

Nomenclature

𝛼 Angle of attack [𝑑𝑒𝑔]

𝛽 Location of a point along the blade span measured from the root [𝑚]

𝜂 Flap deflection angle [𝑑𝑒𝑔]

𝜃 Blade pitch angle [𝑑𝑒𝑔]

𝜆 Tip speed ratio [−]

𝜆𝑟 Local tip speed ratio [−]

𝜇 Fluid viscosity [𝑘𝑔 𝑚𝑠⁄ ]

𝜈 Kinematic viscosity [𝑚2 𝑠⁄ ]

𝜌 Fluid density [𝑘𝑔 𝑚3⁄ ]

𝜎 Solidity [−]

𝜎𝛽 Mechanical Stress [𝑁 𝑚2⁄ ]

𝜎𝑟 Standard deviation of measurements

Φ Coning angle [𝑑𝑒𝑔]

𝜑 Relative velocity angle [𝑑𝑒𝑔]

Ω Rotor angular velocity [𝑟𝑎𝑑 𝑠⁄ ]

𝜔 Wind angular velocity [𝑚 𝑠⁄ ]

𝐴 Projected airfoil area [𝑚2]

𝐴𝑐 Cross-sectional area [𝑚2]

𝑎 Axial induction factor [−]

𝑎′ Tangential induction factor [−]

𝑎𝑐 Critical angle of attack (tip loss correction) [𝑑𝑒𝑔]

𝐵 Number of blades [−]

𝑏𝑟 Bias error

xvii

𝐶𝑑 Drag coefficient [−]

𝐶𝑙 Lift coefficient [−]

𝐶𝑚 Airfoil pitching moment coefficient [−]

𝐶𝑃 Power coefficient [−]

𝐶𝑇 Thrust coefficient [−]

𝐶𝑥 Axial force coefficient [−]

𝐶𝑦 Tangential force coefficient [−]

𝑐 Airfoil chord length [𝑚]

𝐷 Drag force [𝑁]

𝐸 Modulus of elasticity [𝑁 𝑚2⁄ ]

𝐹 Prandtl’s tip loss factor [−]

𝐹𝐷 Blade element drag force [𝑁]

𝐹𝐿 Blade element lift force [𝑁]

𝑓1 Fundamental natural frequency [𝐻𝑧]

𝐼𝑏 Area moment of inertia [𝑚4]

𝐿 Lift force [𝑁]

𝐿𝑒 Effective length [𝑚]

𝑀 Airfoil pitching moment [𝑁𝑚]

𝑀𝛽 Bending moment at point 𝛽 [𝑁𝑚]

𝑚 Mass [𝑘𝑔]

𝑃 Rotor power [𝑊]

𝑝𝑟 Precision error [%]

𝑄 Torque [𝑁𝑚]

𝑅𝑒 Reynolds number [−]

𝑟 Blade radius (span) [𝑚]

𝑈 Freestream wind velocity [𝑚 𝑠⁄ ]

𝑢𝑟 Total uncertainty [%]

𝑟𝑔 Radius of gyration [𝑚]

𝑇 Thrust force [𝑁]

𝑈𝑟𝑒𝑙 Relative velocity [𝑚 𝑠⁄ ]

xviii

Acronyms

2D Two-dimensional

3D Three-dimensional

BEM Blade element theory

CSA Canadian Standards Association

DBR Dynamic brake resistor

HAWT Horizontal axis wind turbine

NACA National Advisory Committee for Aeronautics

NREL National Renewable Energy Laboratory

NWTC National Wind Technology Center

TEF Trailing edge flaps

VFD Variable frequency drive

1

Chapter 1

Background

1.1 Introduction

Wind mills traditionally converted wind power into a usable mechanical form that could provide torque for

activities such as grinding and pumping. Wind turbines developed from wind mills with a similar purpose;

to convert wind power into electrical power. The work on wind turbine development focuses on building

more efficient and more economic wind turbines. This resulted in larger rotors being built and more

sophisticated technologies being applied in operating modern wind turbines. One of the strategies to

improve performance and life-span of wind turbines is active flow control. Active flow control involves the

modification of the aerodynamic characteristics of a wind turbine blade by means of moveable aerodynamic

control surfaces. The aerodynamic control surface can be the full blade, segments of it or smaller more

distributed surfaces along the blade such as micro tabs and flaps [1]. Pitch control has become one of the

traditional and widely used active flow control methods for wind turbines. It involves regulating the rotor

performance and loads by pitching the full blade to change the relative angles with the flow. Recently,

research has focused on blades that incorporate distributed and embedded intelligent systems of sensors

and actuators instead of single control mechanisms. Such technology is referred to as ‘smart blades’ [2].

Active trailing edge flaps (TEFs) are one of the methods proposed in designing a smart blade. Flaps are

relatively small movable control surfaces that directly modify the lift of a blade or airfoil section. The

ultimate goal of the technology is to reduce the effect of freestream wind fluctuations on the blade load.

The idea to directly control lift on a blade using small movable surfaces was inspired by existing

technology in aircraft and helicopters; from the contribution it made for these applications, it seems

promising [1]. These movable surfaces can achieve significantly high changes in the lift coefficient of the

sections they alter in response to their small deflections [3]. This is an effect of the increase or decrease of

the camber of the airfoil of that section based on the side of deployment as shown in Figure 1.1. These

distributed surfaces are usually operated by separate control mechanisms (sensors and actuators) which

have several advantages compared to traditional full blade pitch systems. They have better structural and

safety features and require less power for activation since they have significantly lower surface inertia than

full span pitch control, mainly due to their size [1]. Lower surface inertia is also pivotal to enable high

frequency control which is required to respond to smaller more frequent wind fluctuations.

2

Figure 1.1 Illustration of a hinged trailing edge flap on an S833 airfoil.

1.2 Project Motivation

Power generation through wind energy is one of the fastest developing renewable energy technologies [4].

As developers compete towards building more cost-effective and efficient wind turbines, several challenges

arise that require new strategies and innovations to overcome [5]. The size of a wind turbine is proportional

to its economic advantage on the long term. The size of current and work-in-progress wind turbines is

quickly increasing, as shown in Figure 1.2. One of the main challenges facing the continually increasing

size of wind turbine blades is the fluctuating loads caused by the natural conditions in which they operate.

The ability to alleviate such loads would allow us to reduce the weight, and increase the size and life-span

of blades. Wind turbines are subject to extreme fatigue load cycles due to the highly fluctuating nature of

the wind resource. Hence, most wind turbine components’ design are governed by fatigue instead of

ultimate loads [6].

Figure 1.2 Wind Turbine diameter size development. Adapted from [5].

+ve

Pressure side

Suction side

‘85 ‘87 ‘89 ‘91 ‘93 ‘95 ‘99‘97 ‘01 ‘03 ‘05 ‘10 ?

.3 .5 1.3 1.6.3 2 4.5 5 7.5 8/101st year of operationRated Capacity (MW)

Airbus A380 Wing span

80m

250m Ø

160 m Ø

126m Ø126 m

Ø112 m

Ø

15 m Ø

.05

Ro

tor

dia

me

ter

(m)

3

Active flow control is one of the methods that can alleviate fatigue load in order to enable larger wind

turbines to use lighter and less material in their blade design and increase the operational-life expectancy

of the rotor and other wind turbine components. Pitch control is one of the traditional and widely used

active flow control methods for large wind turbines. Pitch control has proved to significantly reduce fatigue

load increments due to relatively low frequency variations on the blade conditions caused by yaw error,

wind shear and gusts [7]. Larsen et al. [8] showed that individual pitch can reduce fatigue loads by 25%

and the maximum load on the turbine by 6% when measuring bending moment at the hub. As wind turbines

become larger, however, their blades become heavier and more flexible. This adds more stress on pitch

bearings and increases the response time between the stimulating input and actuation of the active system.

Smaller more distributed control devices can achieve faster response times and require smaller embedded

components. Several computational simulations were carried out by researchers that assessed the ability of

such devices to alleviate load and regulate power as an alternative to full blade pitch systems. The studies

yielded consistently promising but varying results. The differences were usually attributed to different

operating conditions and controller design approaches. In addition, scarce but also promising experimental

studies were carried out to validate the flow control potential of such devices. The computational and

experimental studies and their results are discussed in the following Literature review chapter.

Development of the proposed method will allow developers to build larger wind turbines and more

economic versions of the current sizes in the market, which will positively contribute to further integration

of wind power generation in the global energy system.

1.3 Thesis objectives and outline

The potential of flow control using aerodynamic control devices is strongly supported through modelling

and limited experiments. Upon the review of related studies, it was found that there was significantly more

work done on computational simulations and numerical modelling with solemn experimental validation.

The potential contribution of an experimental platform that can investigate the effects of aerodynamic

control devices in controlled operating conditions was evident.

The first objective of this thesis is to develop an instrumented wind turbine test rig and rotor to enable a

wide-range of experimental set-ups for investigations focusing on TEFs. The second objective is to

demonstrate the capability of the developed systems through a steady state study of the effect of TEFs on

blade load and power production. This study sets a foundation for solid contributions towards experimental

work using operational rotating wind turbines in controlled and realistic conditions.

This thesis covers three main phases. First, the design and building of a wind turbine test rig. Second, the

aerodynamic and structural design and fabrication of a modular customizable blade. Third, an experimental

study of the effect of TEFs on blade load and power production carried out using the developed test rig and

blade. The thesis is organized into seven chapters, starting with this introduction and followed by:

- Chapter 2 Literature Review: Provides an outline of the concepts, terminology and theories that

apply to the investigation and an overview of related work in the field.

4

- Chapter 3 Wind Turbine Test Rig: Discusses the design requirements and constraints of the wind

turbine test rig, the design methodology and outcome, and the manufacturing and assembly of the

wind turbine test rig.

- Chapter 4 Modular 3D Printed Blade: Discusses the aerodynamic and structural design

requirements, the design process and outcome, and the fabrication and assembly of the rotor.

- Chapter 5 Experimental Procedure: Describes the facility and measurement equipment, the

experimental setup, and calculations related to the TEF investigation.

- Chapter 6 Results and Discussion: Presents an overview and a discussion of the results of the

experimental investigation.

- Chapter 7 Conclusion: Provides an assessment of the developed wind turbine test rig and rotor in

light of the study objectives, outlines the conclusions from the findings of the experiment performed,

and recommendations for continuation of future studies.

5

Chapter 2

Literature Review

2.1 Theory

2.1.1 Wind turbine overview

The most common modern design for wind turbines is the horizontal axis wind turbine (HAWT) [9]. A

HAWT is aligned such that the axis of rotation of the wind turbine blade, also known as the rotor, is parallel

to the ground, in normal operating conditions it will also be parallel to the direction of the oncoming

freestream wind. The main subsystems of a HAWT, shown in Figure 2.1, are listed below:

- Rotor. The rotor is the main rotating subsystem of the wind turbine and it consists of the blades and

hub. It is the most important component of a wind turbine from a performance and cost point of view.

The rotor blades are the most critical elements in determining the amount of energy captured by the

wind turbine. A rotor typically accounts for more than 25% of the full cost of a wind turbine system

[10].

- Nacelle and yaw system. The nacelle includes the drive-train and energy conversion systems of the

wind turbine. Typically consisting of a motor/generator, gearbox, drive shaft and bearing and is

supported by the main frame. The yaw system allows the nacelle to rotate around a vertical axis.

- Tower and foundation. The tower provides structural support to the wind turbine systems and places

them at the required height from the ground. Steel tubes, lattice structures and cement towers are

typical for modern wind turbines.

- Balance of electrical systems. These include electrical components other than the motor/generator

such as transformers, power correction capacitors, power electronic converters, cables, switchgears,

etc.

6

Figure 2.1 Main wind turbine components.

Rotor

Hub GeneratorGearboxDrive-train

Nacelle frame/yaw system

Yaw axis

Rotor axis

Nacelle cover

Balance of electrical systems

Foundation

7

2.1.2 Airfoil concepts and terminology

Airfoils are structures with specific cross-sectional geometries that generate mechanical forces from the

relative motion between the structure and the surrounding fluid. Wind turbines use airfoils to generate

torque that drives the generator to produce power. The airfoil properties including the shape, length and

width are determined based on the required aerodynamic performance.

2.1.2.1 Geometry of an airfoil

Figure 2.2 shows the common items that are used to characterize an airfoil. The mean camber line is the

line that passes the mid-points between the top and bottom surfaces. Camber is a measure of the curvature

of airfoil. The chord line is a straight line between the leading and trailing edges. If the chord line and

camber line are the same, the airfoil is symmetric. The angle of attack, 𝛼, is the angle between relative

velocity of the fluid moving around the airfoil and its chord line. The mechanical forces generated by the

movement of the airfoil are dependent on the angle of attack.

Figure 2.2 Airfoil nomenclature.

2.1.2.2 Forces on an airfoil

The flow velocity on the convex side of the airfoil increases and the pressure decreases making it the

‘suction’ side of the airfoil. The opposite happens on the concave side which is called the ‘pressure’ side.

The flow along the surface also creates drag due to viscous friction and pressure distribution. These two

phenomena create a distribution of forces on the surface of the airfoil that are resolved in two main

directions, the lift force and drag force, and a moment, the pitching moment. The forces are resolved at the

aerodynamic center, which is the point where the pitching moment does not vary with the angle of attack

[11]. For symmetric airfoils, the aerodynamic center lies exactly at the quarter-chord from the leading edge,

however, it is still used as an approximation for cambered airfoils [11]. Figure 2.3 shows an illustration of

the resultant airfoil forces.

- Lift force is the resultant perpendicular force to the angle of attack and is caused by the pressure

imbalance on both sides of the airfoil that are parallel to the flow.

- Drag force is the resultant force parallel to the direction of the flow and is caused by both viscous

friction and the pressure imbalance.

Chord, cRelative velocity, Urel

Angle of attack, α

Leading edge Trailing edgeMean camber line

Chord line

Thickness

8

- Pitching moment is a moment caused by the pressure distribution on the airfoil surface that acts

about an axis perpendicular to the airfoil cross-section.

Figure 2.3 Airfoil forces.

An important non-dimensional parameter used to characterize fluid flow is the Reynolds number, Re. the

Reynolds number is the ratio between inertial and viscous forces in a fluid and is defined for airfoils by:

𝑅𝑒 =𝑈𝑐

𝜈=

𝜌𝑈𝑐

𝜇=

𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝑓𝑜𝑟𝑐𝑒

𝑉𝑖𝑠𝑐𝑜𝑢𝑠 𝑓𝑜𝑟𝑐𝑒 2.1

where 𝑈 is the fluid velocity, 𝑐 is the chord length of the airfoil, 𝜌 is the fluid density, 𝜈 is the kinematic

viscosity and 𝜇 is the fluid viscosity. Rotor design uses non-dimensional coefficients for the forces and

moments of a two-dimensional airfoil [9]. The values of these coefficients are determined from wind tunnel

tests as a function of the Reynolds number and angle of attack. They are defined as follows [9]:

The lift coefficient:

𝐶𝑙 =𝐿

12 𝜌𝑈

2𝑐=

𝐿𝑖𝑓𝑡 𝑓𝑜𝑟𝑐𝑒 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ⁄

𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑓𝑜𝑟𝑐𝑒 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ⁄ 2.2

The drag coefficient:

𝐶𝑑 =𝐷

12 𝜌𝑈

2𝑐=

𝐿𝑖𝑓𝑡 𝑓𝑜𝑟𝑐𝑒 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ⁄

𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑓𝑜𝑟𝑐𝑒 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ⁄ 2.3

Urel

α

Chord line

Pitching moment

Lift force

Drag force

Quarter-chord

Aerodynamic center

9

The moment coefficient:

𝐶𝑚 =𝑀

12

𝜌𝑈2𝐴𝑐=

𝑃𝑖𝑡𝑐ℎ𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡

𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡 2.4

where 𝐴 is the projected airfoil area, 𝑐 is the chord and 𝑈 is the freestream fluid velocity. 𝑀 is the pitching

moment, while 𝐿 and 𝐷 are the lift and drag forces per unit length of the span of the airfoil into the page.

The two-dimensional coefficients are based on the assumption that the airfoil span is infinite and the

experiments are designed to measure them such that edge effects are negligible [9].

The slope of the linear part of a typical 𝐶𝑙 curve for airfoils, shown in Figure 2.4, is approximately equal

to 2𝜋/𝑟𝑎𝑑 according to thin airfoil theory [3], however, when a critical α is reached 𝐶𝑙 decreases in a

manner that strictly depends on the airfoil geometry [11]. This is known as the stall point. Stall is a

phenomenon where the boundary layer separates from the upper (suction side) of the airfoil causing a rapid

drop in the lift force.

Thin airfoil theory applies the concepts of circulation, streamlines and pressure distribution around a

transformed shape to predict the airfoil characteristics. It assumes that the airfoil thickness is small

compared to the chord length and only applies to small 𝛼 [12]. The theory provides a useful understanding

of the relationship between 𝐶𝑙, 𝛼 and the airfoil geometry, however, since it breaks down for thicker airfoils

and higher 𝛼 that violate its assumptions, in practice the values are usually obtained from numerical and

computational studies and wind tunnel experiments [12] for all aerodynamic design applications.

Figure 2.4 Typical 𝐶𝑙 vs. 𝛼.

0

0.5

1.5

2.0

5 10 15 20

1.0

αo

Cl

0

10

Three-dimensional effects

A rotor blade in reality is made up of a finite series of airfoils. This creates a finite beam with a pressure

difference between the upper and lower surfaces that generates lift. Flow leakage occurring at the tips cause

the streamlines at the upper and lower surfaces to deflect on opposite sides and a discontinuity is seen in

the tangential velocity at the trailing edge [13]. This jump creates trailing vortices due to the continuous

stream-wise vortices in the wake. The result of these effects is that the actual lift of the three-dimensional

blade is reduced compared to the two-dimensional airfoil at the same 𝛼 and 𝑅𝑒, and the lift has a component

parallel to the direction of the flow, called the induced drag [13].

2.1.3 Aerodynamics of HAWTs

A HAWT extracts mechanical energy from a stream of moving air by means of a rotating disc-like converter

[14]. Assuming only the mass of air going through the disc is affected and a portion of its kinetic energy

is extracted, the mass of air slows down. A boundary surface can then be imagined separating the affected

mass going through the disk-like converter. By extending the boundary upstream and downstream a long

stream-tube of circular cross-section is formed [6]. Since no air flows across the boundary, the mass flow

of the air remains the same through the length of the stream-tube. The cross-sectional area of the stream-

tube will vary with the speed of the mass of air according to continuity.

2.1.3.1 Betz momentum theory

Betz’s momentum theory is based on the modelling of a two-dimensional flow through the converter disk

described above, called the ‘actuator disk’ [14]. The model analysis assumes a control volume whose

boundaries are the stream tube boundary and two cross-sections upstream and downstream of the rotor

plane, as shown in Figure 2.5. The flow passes through the cross sections only. The actuator disk creates a

discontinuity in the pressure of the stream flowing through it and represents the power absorbed by the

wind turbine [6]. This model makes the following assumptions [9]:

- Incompressible steady state flow,

- No frictional drag,

- Infinite number of blades,

- Uniform thrust per unit area,

- No wake-rotation,

- Far upstream and far downstream static pressures are equal to the ambient undisturbed pressure.

11

Figure 2.5 Actuator disk model of a wind turbine.

The influence of the wind turbine on the flow velocity is represented by the axial induction factor (or the

retardation factor) a [15]. The axial induction factor represents the fraction of velocity decrease such that:

𝑈2 = 𝑈3 = 𝑈(1 − 𝑎) 2.5

𝑈4 = 𝑈(1 − 2𝑎) 2.6

where 𝑈2 and 𝑈3 are the velocities at the actuator disk, 𝑈4 is the velocity downstream and 𝑈 is the freestream

velocity as shown in Figure 2.5. Applying linear conservation to the control volume, the net force of the

system can be found. This net force is equal and opposite to the thrust force T which is the axial force on

the wind turbine [9]. Applying Bernoulli’s Equation between the freestream and upstream side of the

actuator disk and again between the upstream and downstream sides, it can be shown that [15] :

𝑇 =1

2𝜌𝐴𝑈2[4𝑎(1 − 𝑎)] 2.7

where A is the area of the actuator or rotor disk and 𝜌 is the fluid density. Thrust is characterized by a

non-dimensional thrust coefficient:

𝐶𝑇 =𝑇

12 𝜌𝑈

2𝐴=

𝑇ℎ𝑟𝑢𝑠𝑡 𝑓𝑜𝑟𝑐𝑒

𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑓𝑜𝑟𝑐𝑒 2.8

Upstream

Downstream

Stream tube boundary

U4U3U2U1

1

2 34

Actuator disk

U

U(1-a)

U(1-2a)

Pu Pd

12

𝐶𝑇 = 4𝑎(1 − 𝑎) 2.9

where 𝐶𝑇 is the coefficient of thrust. The power extracted at the disc 𝑃 is related to the momentum change

and it is equal to the thrust times the velocity at the disc. Applying the first law of thermodynamics it can

be shown that [15]:

𝑃 =1

2𝜌𝐴𝑈3[4𝑎(1 − 𝑎)2] 2.10

Similarly, the coefficient of power that characterizes this rotor disk is equal to:

𝐶𝑃 =𝑃

12

𝜌𝑈3𝐴=

𝑅𝑜𝑡𝑜𝑟 𝑃𝑜𝑤𝑒𝑟

𝑃𝑜𝑤𝑒𝑟 𝑖𝑛 𝑤𝑖𝑛𝑑 2.11

𝐶𝑃 = 4𝑎(1 − 𝑎)2 2.12

where 𝐶𝑃 is the coefficient of power. Equation 2.11 has a maximum at 𝑎 = 1/3. The maximum possible

theoretical 𝐶𝑃 known as the Betz limit becomes:

𝐶𝑃,𝑚𝑎𝑥 =16

27≈ 0.593 2.13

An important conclusion of this is the maximum theoretical power that can be extracted by a rotor, which

is a function of the rotor area 𝐴 and freestream velocity 𝑈 only such that:

𝑃𝑚𝑎𝑥 =1

2𝜌𝐴𝑈3

16

27 2.14

2.1.3.2 Angular momentum and wake rotation

In reality, a rotating blade will additionally impose a spin to the flow in the rotor wake. To conserve angular

momentum, this spin is equal to the torque of the rotor [14]. The Betz momentum theory can be expanded

to include these effects and can be called the general momentum theory. Note that all other assumptions

from Betz theory still apply. An annular stream tube with a radius 𝑟 and a thickness 𝑑𝑟 is applied to the

actuator disk model, as shown in Figure 2.6. the area of the control volume cross-section becomes 2𝜋𝑟𝑑𝑟

[9].

13

Figure 2.6 Annular control volume.

The angular velocity imparted on the flow 𝜔 is assumed to be small compared to the angular velocity of

the rotor Ω such that the pressure in the far wake is equal to the pressure in the freestream. The tangential

induction factor 𝑎′ is a measure of the impact of the rotor rotation on the fluid.

𝑎′ = 𝜔 2Ω ⁄ 2.15

In addition to the axial component, 𝑈(1 − 𝑎), the total induced velocity at the rotor now has a component

in the angular plane 𝑟Ω𝑎′. The tip speed ratio 𝜆 is defined as the ration between the blade tip speed and the

freestream velocity. At the tip:

𝜆 = Ω𝑅/𝑈 2.16

At the control volume radius:

𝜆𝑟 = Ω𝑟/𝑈 2.17

where 𝜆𝑟 is the local tip speed ratio.

By applying conservation of linear momentum, the differential contribution to thrust 𝑇 can be expressed

as:

𝑑𝑇 = [4𝑎(1 − 𝑎)]𝜌𝑈2𝜋𝑟𝑑𝑟 2.18

1

2 34

U U(1-a) U(1-2a)

r

dr

stream tube at rotor disk plane

Ω

14

Similarly by applying conservation of angular momentum the differential contribution to torque 𝑄 can

be expressed as:

𝑑𝑄 = [4𝑎′(1 − 𝑎)]𝜌𝑈𝜋𝑟3𝑑𝑟 2.19

The power generated by each element is equal to the differential torque 𝑑𝑄 multiplied by the angular

rotation of the rotor. Using the definition of the local speed ration in equation 2.17 the differential power

contribution by each segment can be expressed as:

𝑑𝑃 = [4

𝜆2𝑎′(1 − 𝑎)𝜆𝑟

3𝑑𝜆𝑟] 𝜌𝐴𝑈3 2.20

The momentum theory provides an understanding of the flow field and relates it to thrust and power

production of the rotor through the flow induction parameters 𝑎 and 𝑎’. However, it fails to link the rotor

performance to the rotor geometry [15].

2.1.3.3 Blade element theory

The blade element theory determines the forces on the rotor solely by the lift and drag characteristics of the

airfoil. The blade is divided into a finite number of segments (or elements) for the analysis [9]. The lift and

drag forces in an airfoil is a function of its geometry and the relative velocity of the fluid surrounding it as

discussed earlier in section 2.1.2. For a rotating blade, the relative velocity is the resultant of both the

angular and axial velocity as show in Figure 2.7. The blade segment is pitched at an angle 𝜃. The angle of

the 𝑈𝑟𝑒𝑙 vector is 𝜑. 𝑈𝑟𝑒𝑙 can be compared to its counter-part in Figure 2.3 for the lift and drag force

directions.

Figure 2.7 Blade element velocities.

Rotor planeΩr(1+a’)

U(1-a)

Urel ϕ

α

θ

dFLdFD

15

The angle of attack of the segment is:

𝛼 = 𝜑 − 𝜃 2.21

The principle blade element theory assumption is that the forces acting on the blade segment are identical

to the forces on a two-dimensional airfoil with the same geometry. The pitch angle 𝜃 is modified along the

blade to acquire 𝛼 that has the desired 𝐶𝑙 and 𝐶𝑑 values based on known sets of data from wind tunnel

experiments as discussed in section 2.1.2. The following relations can also be deduced from Figure 2.7:

tan 𝜑 =𝑈(1 − 𝑎)

Ω𝑟(1 + 𝑎′) 2.22

𝑈𝑟𝑒𝑙 =

𝑈(1 − 𝑎)

sin 𝜑 2.23

The differential contribution to lift and drag can be acquired for each blade segment by the resolving the

lift and drag forces based on the airfoil data into the thrust and torque directions, as shown in Figure 2.8.

Figure 2.8 Blade element forces.

The axial thrust on the blade segment becomes [6]:

𝑑𝑇 =1

2𝜌𝑈𝑟𝑒𝑙

2 𝐵𝑐(𝐶𝑙 cos 𝜑 + 𝐶𝑑 sin 𝜑)𝑑𝑟 2.24

dFL

dFD

Rotor plane

dT

ϕ

Urel

dQ

x

y

16

where 𝑑𝑟 is the segment thickness, 𝐵 is the number of blades and 𝑐 is the cord length. The torque on the

blade segment becomes [6]:

𝑑𝑄 =1

2𝜌𝑈𝑟𝑒𝑙

2 𝐵𝑐𝑟(𝐶𝑙 sin 𝜑 − 𝐶𝑑 cos 𝜑)𝑑𝑟 2.25

An important conclusion is that an increase in 𝐶𝑙 leads to an increase in both the torque and the thrust,

while an increase of 𝐶𝑑 leads to a decrease in torque but an increase thrust. The blade element theory

provides a definition for the thrust and torque of a blade segment as a function of the flow angles and blade

characteristics. Noting that the blade segment in a rotating frame is a representation of the control volume

used in the momentum theory (as in Figure 2.6), the two theories are combined to be used to design the

ideal blade shape or to analyze the performance of a blade with any arbitrary shape [9].

2.1.3.4 Blade element momentum (BEM) theory

The BEM theory couples the momentum theory with local effects at the actual blades represented by the

blade element theory. In this method the influence of the flow field on the aerodynamic response of the

blade segments is analyzed. The BEM model is capable of calculating the steady loads, torque and power,

for different settings of freestream velocity, angular blade velocity and pitch angles [13], while accounting

for the finite number of blades and their airfoil characteristics along their radius. This is achieved by

equating the force relationships concluded from the momentum theory, equations 2.18 and 2.19 with the

force relations concluded from the blade element theory, equations 2.24 and 2.25. This produces a

relationship between the induction factors, 𝑎 and 𝑎’, and the blade characteristics for the given flow, 𝐶𝑙 and

𝐶𝑑. The relationships are applied at the radius of the control volume at each segment:

𝑎 =

1

4 sin2 𝜑𝜎𝐶𝑥

+ 1

2.26

and

𝑎′ =

1

4 sin 𝜑 cos 𝜑𝜎𝐶𝑦

− 1

2.27

where 𝜎 is defined as the solidity at radius 𝑟. Solidity accounts for the finite number of blades.

𝜎 =𝑐𝐵

2𝜋𝑟 2.28

17

𝐶𝑥 and 𝐶𝑦 are the resolutions of the 𝐶𝑙 and 𝐶𝑑 in the direction of the axial and tangential force as shown in

Figure 2.8, so that:

𝐶𝑥 = 𝐶𝑙 cos 𝜑 + 𝐶𝑑 sin 𝜑 2.29

𝐶𝑦 = 𝐶𝑙 sin 𝜑 − 𝐶𝑑 cos 𝜑 2.30

In designing an optimized rotor for specified flow conditions, a BEM algorithm solves these equations

iteratively for each radial segment of the control volume to achieve the ideal values of 𝑎 and 𝑎’. For

analyzing a known rotor for a range of flow conditions, freestream wind speeds for example, a sweep of

the iterative process is performed on discrete values of the entire range to predict the performance curves

of the rotor. Details of the iteration steps can be found in [13].

The overall coefficient of power and coefficient of torque, 𝐶𝑃 and 𝐶𝑇, are the standard parameters

that are used to characterize and compare different rotor performance [6]. Using the values of 𝑎 and 𝑎’ from

the BEM algorithm output, 𝐶𝑃 and 𝐶𝑇 can be calculated by integrating the power and torque contributions

from each blade segment [15].

𝐶𝑃 = ∫ ΩdQ

𝑅

0

12

𝜌𝜋𝑅2𝑈3 2.31

𝐶𝑇 = ∫ dT

𝑅

0

12 𝜌𝜋𝑅

2𝑈2 2.32

where 𝑅 is the rotor radius. Figure 2.7 shows an example of a 𝐶𝑇 and 𝐶𝑃 curve for an ideal rotor.

18

Figure 2.9 𝐶𝑃 and 𝐶𝑇 for an ideal HAWT vs. axial induction factor 𝑎 [13].

2.1.3.5 Limitations and corrections

The BEM model is agreed to be a suitable for the design and analysis of a modern HAWT [6], [9]. However,

the design has limitations and several corrections have been suggested to improve its accuracy. Two

important effects that must be accounted for are tip losses and high values of the axial induction factor.

Prandtl’s tip loss factor. For a rotor with finite blades the vortices produced in the wake are different from

those produced by a rotor with a finite number of blades. Prandtl’s tip loss factor accounts for the

assumption of infinite number of blades made by the momentum theory. A correction factor derived by

Prandtl is applied to the differential force equations of the momentum theory such [13]:

𝑑𝑇 = [4𝑎(1 − 𝑎)]𝜌𝑈2𝜋𝑟𝐹𝑑𝑟 2.33

and

𝑑𝑄 = [4𝑎′(1 − 𝑎)]𝜌𝑈𝜋𝑟3𝐹𝑑𝑟 2.34

where 𝐹 is the the tip loss factor and is computed as follows [9]:

𝐹 = (2

𝜋) cos−1 [exp (− {

(𝐵 2⁄ )[1 − (𝑟 𝑅)⁄

(𝑟 𝑅)⁄ sin 𝜑})] 2.35

10.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.8

0.2

1

0.4

0.6

CT

CP

a

19

𝐹 varies with 𝜑 and is unique to the flow conditions. Equations 2.18 and 2.19 should be replaced by 2.33

and 2.34 in the execution of the BEM algorithm, and a step for the calculation of 𝐹 should be added.

Glauert correction. The general momentum theory breaks down at a critical value of 𝑎=0.4, known as 𝑎𝑐.

An empirical relationship between 𝐶𝑇 and a has been made to fit with measurements and is used for high

induction values [13]:

𝐶𝑇 = {4𝑎(1 − 𝑎)𝐹, 𝑎 < 𝑎𝑐

4(𝑎𝑐2 + (1 − 2𝑎𝑐)𝑎)𝐹, 𝑎 ≥ 𝑎𝑐

2.36

where 𝐹 is the tip loss factor. By equating to the differential thrust equation on an annular segment, the

axial induction factor for 𝑎 > 𝑎𝑐 becomes [13]:

𝑎 =1

2[2 + 𝐾(1 − 2𝑎𝑐 ) − √(𝐾(1 − 2𝑎𝑐) + 2)

2 + 4(𝐾𝑎𝑐2 − 1)] 2.37

where:

𝐾 =4𝐹𝑠𝑖𝑛2𝜑

𝜎𝐶𝑥 2.38

In order to compute the velocities correctly for cases where 𝑎 > 𝑎𝑐 equation 2.37 should replace

equation 2.26 in the BEM algorithm.

2.1.3.6 PROPID Design code

PROPID [16] is a computer program code based on a multipoint inverse design method [17] for the design

and analysis of horizontal axis wind turbines [18]. PROPID uses the PROPSH BEM code [19], which is an

updated version of the PROP code [20], for its analysis. The codes are based on the BEM equations and

algorithm discussed in the previous sections. PROPID allows the user to specify different BEM correction

models from the theory to be applied in the analysis. Table 2.1 shows some of the models that can be

activated during analysis.

The strength of the code is its inverse design capability. Inverse design allows the specification of the

required design operating conditions and the iterative algorithm is used to modify the input parameters

(geometric blade characteristics) to achieve the required performance. The number of input parameters the

user allows the program to change should be equal to the number of performance characteristics specified.

For example, if the program is required to achieve peak 𝐶𝑝 at a specific rotation speed and wind speed, it

can optimize the blade pitch and chord length. PROPID also allows for the specification of distributions to

be used as optimization targets, as long as another equal number of distributions are determined by the

20

code. For example, the required axial induction distribution at the design point can be specified as a target,

and the code is left to optimize the blade twist and chord length for each segment [18]. In contrast, PROPID

is also capable of analyzing the off-design aerodynamic capabilities of a rotor with fully specified geometry

(chord, twist and airfoil distributions and blade number) to predict the rotor performance in different

operating conditions. Table 2.1 shows the basic user input for the analysis case. In the design case, some of

the input parameters are left for the code to optimize, details can be found in [18].

Category Parameter Setting

Operating conditions

Wind speed float

Rotation speed float

Blade pitch float

Input Parameters

Blade length float

Hub height float

Number of blades integer

Hub cutout float

Chord and twist distribution

Airfoil distribution

Rotor cone angle float

Aerodynamic Models

Tip loss model On/off

Hub loss model On/off

Brake state model On/off

Viterna stall model On/off

Wake Swirl On/off

Table 2.1 PROPID primary user specified parameters for analysis case [18].

The aerodynamic models are based on empirical equations from the different corrections to the BEM

algorithm. The tip and hub loss models are based on Prandtl’s corrections discussed in the previous section.

The brake state model applies a modified version of the Glauert correction for high induction factors. The

Viterna stall model applies an approximation to the aerodynamic characteristics of the airfoil when

calculating the post-stall performance of the rotor. The wake swirl model is a correction that accounts for

the angular momentum.

21

Typical output parameters from a PROPID wind sweep analysis are shown in Table 2.2. For a detailed

and complete list of output parameters and their organization see [18].

Category Parameter Range

Aerodynamics

𝐶𝑙 distribution Radial position

𝐶𝑑 distribution Radial position

𝛼 distribution Radial position

Performance

Rotor power Wind speed

𝐶𝑃 Tip speed ratio

Thrust Wind Speed

Table 2.2 PROPID analysis output.

2.1.4 Wind Turbine Loads

Wind turbine loads are forces or moments that act upon the wind turbine. The loads are predominantly

dependent on the interaction between the rotor and the wind. In designing the rotor, although it is helpful

to maximize the loads that operate the rotor for extraction of useful energy, this also increases the stresses

that the wind turbine components must endure. Due to the varying nature of the wind, the stresses on the

wind turbine components can be highly dynamic. The structural design of wind turbine components should

satisfy two major requirements. First, they should be able to withstand the extreme expected loads. Second,

they should be designed such that the fatigue life of their components is guaranteed for their service life

which is typically between 20 and 30 years [14]. Accounting for fatigue is especially important since fatigue

loading on wind turbine blades is the major factor that contributes towards structural failure [6]. Different

loads can be categorized according to their temporal effect on the rotating rotor, as shown in Figure 2.10.

- Steady loads. Steady loads are those that do not vary over long periods of time. Steady loads can

be an effect of interaction of wind with static or rotating components of the wind turbine.

- Cyclic loads. Unsteady loads that vary with a regular pattern over time, or are periodic in nature

are called cyclic loads. They can be a result of wind shear, gravity or off-wind yaw motion.

- Non-cyclic loads. Loads that are transient in nature and vary with time over relatively short periods

without following a specific pattern are called non-cyclic loads. Examples of such loads are the

stochastic loads that are caused by wind turbulence and sudden inertial loads caused by the rotor

when it is accelerating for start-up or decelerating upon applying brakes.

22

Aerodynamic forces Inertial and gravity forces

Ste

ady l

oad

s

Steady mean wind speed Centrifugal forces

Unst

eady l

oad

s

Cycl

ic l

oad

s

Vertical wind shear Cross wind (yaw) Gravity forces

No

n-c

ycl

ic l

oad

s

Wind turbulence

Figure 2.10 Aerodynamic, gravitational and inertial loads that affect a HAWT blade. Adapted from [14].

23

The sources of each of the loads in each of these categories can be aerodynamic or inertial. Aerodynamic

loads are the product of the interaction between the rotor and wind. Since the loads are responsible for

power generation and structural stresses, controlling aerodynamic loads can be very beneficial in improving

the performance of the wind turbine rotor or limiting transformation of freestream wind effects into load

changes within the blade structure. As discussed in previous sections (see equations 2.24-2.27), it is evident

that 𝐶𝑙 is the major factor in determining the differential torque and thrust contribution of the series of blade

segments that make the full blade. Although the blade geometry, thus the distribution of 𝐶𝑙, is optimized

for the peak performance at the design conditions, off-design performance could be improved by modifying

the aerodynamic properties. There are several ways of controlling the aerodynamics loads that all depend

on the modification of the aerodynamic performance of a blade, they all rely on modifying 𝐶𝑙 of the full

blade or different blade segments. Since 𝐶𝑙 is a result of the blade geometry and a function of 𝛼 it can be

modified either by changing 𝛼, by pitching the blade segment or changing the rotation speed (see

Figure 2.7), or by changing the geometry of the blade segment.

2.1.5 Aerodynamic load distribution on HAWT blades

The aerodynamic load distribution over the span of a HAWT wind turbine blade is the result of the

collective contribution to the blade loads by the series of airfoils that form the blade geometry. The result

of the integration of the differential torque (equations 2.24) is the tangential load distribution which creates

a power-producing moment on the blade in the edgewise (in-plane) direction. Gravitational forces on the

blades are cyclic loads that also contribute to the edgewise moment. The integration of the differential thrust

(equation 2.25) produces the axial force distribution which acts in the flapwise (out-of-plane) direction. The

flapwise bending moment resulting from the axial forces is of considerably more significance on the blade

strength and will be discussed in more detail. Figure 2.11 shows the lift and drag forces on an airfoil section

and the result of their integration along the blade length, it also shows the coordinates and terms used for

identifying the load directions.

The distribution profile for the axial and tangential force distributions for different wind speeds can vary

distinctly for a blade with local twist angles and different airfoils along its span. This is related to the airfoil

characteristics. Although they vary uniformly with 𝛼 in the normal range of operation, a change in the

airfoil geometry or twist angle can cause a change in local load contributions. The twist is optimized for

the design wind speed for a load distribution to be as close to the theoretical maximum as possible. This

distribution can significantly change especially for higher 𝛼 if the flow separates creating stall at some

segments for the blade. Figure 2.12 shows the tangential and axial distributions for a WKA-60 turbine blade

[14] based on a simulation. The wind turbine’s rated speed is 12.2m/s. The distributions can be seen to

become significantly distorted beyond rated conditions. Also the maximum axial force within the normal

operation range is six times greater than the maximum tangential force, hence the significance of flapwise

bending moment.

24

Figure 2.11 Rotor forces co-ordinates and technical terms. Adapted from [14].

Flapwise direction

Edgewise Direction

chord

Tangential force distribution

Axial force distribution

Rotor plane

α

Free stream wind, U

y

z

Urel

x

Ωr(1+a’)

U(1-a)

θ

ϕ

dFD

dFL

25

Figure 2.12 Modelled tangential (top) and axial (bottom) force distribution for WKA-60 turbine blade [14].

12.2 m/s (rated)

0 0.2 0.4 0.6 0.8 1

1600

1200

800

400

0

-400

r/R

Tan

gen

tial

fo

rce

dis

trib

uti

on

N/m

9 m/s

24 m/s

Axi

al f

orc

e d

istr

ibu

tio

n N

/m

12.2 m/s (rated)

0 0.2 0.4 0.6 0.8 1

4000

3000

2000

1000

0

-1000

r/R

9 m/s24 m/s

26

2.1.5.1 Effect of coning on rotor load and performance

Thrust loading on a rotor can cause the blade to bend in the flapwise direction creating an angle with the

typical rotation plane. This deflection, shown in Figure 2.13 is called coning. Since the parameters used for

velocity calculations are measured at right angles to the rotor axis, a modification is applied to the airfoil

velocities in order to account for the effect of coning on the 𝐶𝑇 and 𝐶𝑃 and ultimately the rotor torque and

thrust loads. The incoming freestream velocity, 𝑈, is reduced by the cosine of the coning angle Φ [15].

Figure 2.13 Schematic showing the coning angle Φ.

Recalling equation 2.23, the relative velocity 𝑈𝑟𝑒𝑙 for a blade experiencing coning becomes [15]:

𝑈𝑟𝑒𝑙 =

𝑈 cos Φ (1 − 𝑎)

sin 𝜑 2.39

where Φ is the coning angle measured from the plane of rotation. Substituting the new 𝑈𝑟𝑒𝑙 definition into

the differential thrust definition (equation 2.24) from the blade element theory gives the new contribution

to torque from each blade segment as:

𝑑𝑇 =1

2𝜌𝐵𝑐𝑈2(1 − 𝑎)2

cos2 Φ

sin2 𝜑(𝐶𝑙 cos 𝜑 + 𝐶𝑑 sin 𝜑)𝑑𝑟 2.40

The same can be applied to the torque contribution of blade segments by substituting the modified 𝑈𝑟𝑒𝑙

into the differential torque definition (equation 2.52.25) from the blade momentum theory:

Rotor axial load

Rotation plane

Free stream wind

Top view of the rotor

Φ

27

𝑑𝑄 =1

2𝜌𝐵𝑐𝑈2(1 − 𝑎)2

cos2 Φ

sin2 𝜑(𝐶𝑙 sin 𝜑 − 𝐶𝑑 cos 𝜑)𝑟𝑑𝑟 2.41

An important conclusion is that the coning angle reduces the thrust and torque contribution by a blade

segment by the square of the cosine of the angle. In contrast, reducing the coning angle would increase both

the power and torque production.

2.1.5.2 Flapwise bending moment

A wind turbine blade u